The Magic of Logic (1)
Recently Enders, my beautiful grandson, turned six. He is a bright boy with extraordinary linguistic skills. And a very astute grasp of things, like missing planets and deadly dangerous butterflies. But one thing he had not encountered yet was logical puzzles, like the ones I had brought up his father with. So it was high time.
“Enders,” I said on his birthday, “on an island there are three kinds of people: knights, who always tell the truth; knaves, who always lie, and jokers, who sometimes lie and sometimes tell the truth. I met a man there and asked him what he was. ‘I’m a knave,’ he replied. So what was he, really?”
Enders looked at me in fascination. Clearly I was expecting him to say something, so he did: “And you punched him!” No, no, you must tell me what the man is! It took a while and a little back-and-forth for Enders to understand the concept: he was expecting a story, some continuation of the narrative, not a puzzle for him to solve. But then he got it: “No, he’s not a knave, because then what he said would be true, and knaves are liars. So he must be a knight… Hey, wait a minute, he can’t be that, because then he would have told a lie, and knights always tell the truth.” It took him a minute or two after that to come up with the solution: “He’s a joker! And he is telling a lie!”
It is not easy for me to describe how his face lit up, the joy he obviously felt in finding the solution. When his parents got home he rushed over to them and gave them the puzzle. And he asked me for more.
The second one was the well-known problem of the farmer who needs to transport a wolf, a lamb and some hay across a river, but has a boat that can only take one at a time. We set thing up with different coloured Legos and a band of paper depicting the river.
Enders decided to start with the wolf, which he transferred onto a Lego boat and moved across the river. Then came back and said: “Hey, where’s the hay?” He was looking for the yellow Lego I had removed. “The lamb ate it all,” I told him. Ahh, so that doesn’t work. :-(
Enders tried all combinations, but could not find a way. Always bad things happened. He was stumped.
The impressive thing was that he sat there thinking. His eyes wandered across the room, he looked at the wall, at me, out the window. For maybe five or six minutes. That is when I decided to help him. “The farmer can transport things both ways, Enders.” After that it took him two minutes to work it out: “Wait, I’ve got it: first the hay… No, then the wolf eats the lamb. So first the lamb, because, ha-ha-ha, wolves don’t eat hay. Then the hay, and he brings back the lamb, and then he takes the wolf across, and then goes back to fetch the lamb!!” Once again pure joy in his face — he even worked out a second solution: first the lamb (the only way), then the wolf, bring the lamb back, take the hay across, and then fetch the lamb. This is so great, gimme more!
Enders’ brother Hennes, four years old, was unable to solve the puzzles I was giving Enders; but he listened carefully, and understood the logic. And when the parents came home, Hennes was the one who could repeat the problem more succinctly. Enders tended to miss some details in his rush to challenge his parents. Hennes, on the other hand, repeated everything with utmost precision — and gave the solution with equal clarity.
I kept bringing more puzzles, and observed a wonderful phenomenon: Enders became progressively more affectionate towards me. He rushed over when we picked him up from daycare, hugging me and calling me “dear pardner” and things. The point is that nothing had changed between us, except the logical puzzles. Clearly that was causing the steep rise in his affection.
So one day recently I told the above story to Bettina, a neighbour who sometimes invites us to a sumptuous breakfast. She is a teacher at a local school. A few weeks later Bettina came over to our place, together with Cornelia, a colleague. They told me they had a program for exceptionally talented students in their school, and that it was imperative that I start doing a course of logical puzzles with them. Bettina had a title for it: The Magic of Logic — some of my puzzles involve magical tricks. How about four sessions for a start? I agreed, although I am currently in the process of trying to retire after more than twenty years of producing a very extensive news page for my chess software company. I wanted to concentrate mainly on the grandsons and on this biographical and general interest blog. But hey, it may work out perfectly: I start with the first session at the school next Tuesday, and will, I promise, report here on how I get along. It is really worthwhile — showing young children the joys of logical thinking. Let’s see how older students react.
Related stories from my blog:
- Part two of The Magic of Logic series
- Remembering Martin Gardner
- Lie to your kids — it’s good for them
- The Café Wall Illusion
- Prime number cicadas — really!
- Money problems without decimals
- IQ test: weighing the coins
- Tricking the brain
- Scamming programmers with Guess
- The art of skepticism
- He had a dream — a logical puzzle
I am bound to use some of the above in the Magic of Logic lessons.